[CLN-list] roundoff errors due to changes in the binary splitting algorithm?

[Alexei Sheplyakov]

Hello!

On Sat, Jan 19, 2008 at 11:34:24PM +0100, Richard B. Kreckel wrote:

> The second reason is that while 
> performing the binary splitting, some intermediate integer results may 
> become much larger than the result's precision warrants.  As it turns 
> out, that excess precision can simply be truncated by coercing the 
> result into a cl_LF of appropriate length.  Basically, this compresses 
> the extra digits into the floating-point exponent.

Can you prove this won't result in an additional roundoff error?

> With some rational series, the savings are dramatic.  As an extreme example,
> attached is a picture of the memory footprint when computing one million decimal 
> digits of Euler's gamma.  The red curve corresponds to CLN-1.1.x while 
> the blue one to CLN 1.2.0.  Here, making the operands smaller even saves 
> computing time.

What about the accuracy of the result?

Best regards,
	Alexei

-- 
All science is either physics or stamp collecting.

-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 827 bytes
Desc: Digital signature
Url : http://www.cebix.net/pipermail/cln-list/attachments/20080120/c94c3153/attachment-0001.pgp